Finite Group Databasebeta

← Group #10945055

Character table — Group #10945055

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888812121212121212121212121212121212161616161616242424244848
order1222222234444666666622444444444412121212121212126688881212121212121212242424242424242444444444444444444412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11-111-1-111-1-11-1
χ1011111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111-111-1-1-1-111-11
χ1111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-11-1-111-1-111-11
χ1211111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-11-1-11111-1-11-1
χ1311111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-11-1-11111-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-11-1-111-1-1111-1
χ1511111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-111111-111-1-1-1-1111-1
χ1611111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-11-111-1-111-1-1-11
χ17222222222-2-2-2-222222222200000000-2-2-2-2-2-2-2-2-2-2220000000000000000000022-2-2-2-22200000000000000000000
χ18222222222-2-2-2-222222222200000000-2-2-2-2-2-2-2-2-2-22200000000000000000000-2-22222-2-200000000000000000000
χ19222222222-2-2-2-22222222-2-20000000022-2-22222-2-2-2-2000000000000000000002222-2-2-2-200000000000000000000
χ20222222222-2-2-2-22222222-2-20000000022-2-22222-2-2-2-200000000000000000000-2-2-2-2222200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000-2-21111000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1222211111111-1-1-1-1-1-1-1-10000000000000000-2-21111000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111000000000000000022-1-1-1-1000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-1-11111-1-11122-2-2-1-1-1-11111-1-1-1-1111100000000000000002-2-1-111000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-1-11111-1-111-2-222-1-1-1-111111111-1-1-1-10000000000000000-2211-1-1000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-2-2-1-11111-1-11122-2-21111-1-1-1-1-1-1-1-111110000000000000000-2211-1-1000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-2-2-1-11111-1-111-2-2221111-1-1-1-11111-1-1-1-100000000000000002-2-1-111000000
χ2922-22-2-2-2222-22-22-222-2-2-20000002i2i−2i−2i002-200002-200000000002i2i−2i−2i000000002i−2i002i−2i00000022-2-2000000000000
χ3022-22-2-2-2222-22-22-222-2-2-20000002i2i−2i−2i002-200002-200000000002i2i−2i−2i00000000−2i2i00−2i2i000000-2-222000000000000
χ3122-22-2-2-2222-22-22-222-2-2-2000000−2i−2i2i2i002-200002-20000000000−2i−2i2i2i000000002i−2i002i−2i000000-2-222000000000000
χ3222-22-2-2-2222-22-22-222-2-2-2000000−2i−2i2i2i002-200002-20000000000−2i−2i2i2i00000000−2i2i00−2i2i00000022-2-2000000000000
χ3322-22-2-2-222-22-222-222-2-2-2002i2i−2i−2i000000-220000-220000002i2i−2i−2i0000000000002i−2i00−2i2i0022-2-20000000000000000
χ3422-22-2-2-222-22-222-222-2-2-2002i2i−2i−2i000000-220000-220000002i2i−2i−2i000000000000−2i2i002i−2i00-2-2220000000000000000
χ3522-22-2-2-222-22-222-222-2-2-200−2i−2i2i2i000000-220000-22000000−2i−2i2i2i0000000000002i−2i00−2i2i00-2-2220000000000000000
χ3622-22-2-2-222-22-222-222-2-2-200−2i−2i2i2i000000-220000-22000000−2i−2i2i2i000000000000−2i2i002i−2i0022-2-20000000000000000
χ372-22-22-2-2222-2-22-222-22-2-2002i−2i2i−2i000000-2200002-20000002i−2i2i−2i000000000000002i−2i002i−2i00002-22-2000000000000
χ382-22-22-2-2222-2-22-222-22-2-2002i−2i2i−2i000000-2200002-20000002i−2i2i−2i00000000000000−2i2i00−2i2i0000-22-22000000000000
χ392-22-22-2-2222-2-22-222-22-2-200−2i2i−2i2i000000-2200002-2000000−2i2i−2i2i000000000000002i−2i002i−2i0000-22-22000000000000
χ402-22-22-2-2222-2-22-222-22-2-200−2i2i−2i2i000000-2200002-2000000−2i2i−2i2i00000000000000−2i2i00−2i2i00002-22-2000000000000
χ412-22-22-2-222-222-2-222-22-2-20000002i−2i2i−2i002-20000-2200000000002i−2i2i−2i00000000002i−2i00−2i2i2-22-20000000000000000
χ422-22-22-2-222-222-2-222-22-2-20000002i−2i2i−2i002-20000-2200000000002i−2i2i−2i0000000000−2i2i002i−2i-22-220000000000000000
χ432-22-22-2-222-222-2-222-22-2-2000000−2i2i−2i2i002-20000-220000000000−2i2i−2i2i00000000002i−2i00−2i2i-22-220000000000000000
χ442-22-22-2-222-222-2-222-22-2-2000000−2i2i−2i2i002-20000-220000000000−2i2i−2i2i0000000000−2i2i002i−2i2-22-20000000000000000
χ452-2-2-2-2222222-2-2-2-22-2-2222-2000000002-2-2-222-2-2222-200000000000000000000000000002-2-222-2-22000000000000
χ462-2-2-2-2222222-2-2-2-22-2-2222-2000000002-2-2-222-2-2222-20000000000000000000000000000-222-2-222-2000000000000
χ472-2-2-2-2222222-2-2-2-22-2-222-2200000000-22-2-2-2-22222-2200000000000000000000000000002-2-22-222-2000000000000
χ482-2-2-2-2222222-2-2-2-22-2-222-2200000000-22-2-2-2-22222-220000000000000000000000000000-222-22-2-22000000000000
χ492-2-2-2-22222-2-222-2-22-2-2222-22-2-22-222-2-2222-2-222-2-22-200002-2-22-222-2000000000000000000000000000000000000
χ502-2-2-2-22222-2-222-2-22-2-2222-2-222-22-2-22-2222-2-222-2-22-20000-222-22-2-22000000000000000000000000000000000000
χ512-2-2-2-22222-2-222-2-22-2-222-222-2-222-2-222-22222-2-2-2-2-2200002-2-222-2-22000000000000000000000000000000000000
χ522-2-2-2-22222-2-222-2-22-2-222-22-222-2-222-22-22222-2-2-2-2-220000-222-2-222-2000000000000000000000000000000000000
χ532-2-2-2-2222-1-2-22211-111-1-12-22-2-22-222-2-22-1-111-1-111-110000-111-11-1-1133−3−333−3−30000000000000000003−33−3000000
χ542-2-2-2-2222-1-2-22211-111-1-12-22-2-22-222-2-22-1-111-1-111-110000-111-11-1-11−3−333−3−333000000000000000000−33−33000000
χ552-2-2-2-2222-1-2-22211-111-1-12-2-222-22-2-22-22-1-111-1-111-1100001-1-11-111-133−3−333−3−3000000000000000000−33−33000000
χ562-2-2-2-2222-1-2-22211-111-1-12-2-222-22-2-22-22-1-111-1-111-1100001-1-11-111-1−3−333−3−3330000000000000000003−33−3000000
χ572-2-2-2-2222-1-2-22211-111-1-1-222-2-222-2-222-2-1-1-1-111111-10000-111-1-111-133−3−3−3−3330000000000000000003−3−33000000
χ582-2-2-2-2222-1-2-22211-111-1-1-222-2-222-2-222-2-1-1-1-111111-10000-111-1-111-1−3−33333−3−3000000000000000000−333−3000000
χ592-2-2-2-2222-1-2-22211-111-1-1-22-222-2-222-22-2-1-1-1-111111-100001-1-111-1-1133−3−3−3−333000000000000000000−333−3000000
χ602-2-2-2-2222-1-2-22211-111-1-1-22-222-2-222-22-2-1-1-1-111111-100001-1-111-1-11−3−33333−3−30000000000000000003−3−33000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000-4-422222222-2-2000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000004422-2-2-2-22222000000000000000000000000000000000000000000000000
χ63444-4-4-44-44000044-4-4-44-400000000000000000000000000000000000000000000000000000000000000000022−2200
χ64444-4-4-44-44000044-4-4-44-4000000000000000000000000000000000000000000000000000000000000000000−222200
χ6544-44-4-4-44-24-44-4-22-2-22220000004i4i−4i−4i00-220000-220000000000−2i−2i2i2i000000000000000000000000000000000000
χ6644-44-4-4-44-24-44-4-22-2-2222000000−4i−4i4i4i00-220000-2200000000002i2i−2i−2i000000000000000000000000000000000000
χ6744-44-4-4-44-2-44-44-22-2-2222004i4i−4i−4i0000002-200002-2000000−2i−2i2i2i0000000000000000000000000000000000000000
χ6844-44-4-4-44-2-44-44-22-2-222200−4i−4i4i4i0000002-200002-20000002i2i−2i−2i0000000000000000000000000000000000000000
χ6944-4-444-4-4400004-4-4-44-4400000000000000000000000022−2200000000000022−2222−220000000000000000000000000000
χ7044-4-444-4-4400004-4-4-44-44000000000000000000000000−2222000000000000−2222−22220000000000000000000000000000
χ7144-4-444-4-4-20000-2222-22-20000000000000023−2323−2300000022−22000000006−66−6−22−220000000000000000000000000000
χ7244-4-444-4-4-20000-2222-22-20000000000000023−2323−23000000−222200000000−66−662−22−20000000000000000000000000000
χ7344-4-444-4-4-20000-2222-22-200000000000000−2323−232300000022−2200000000−66−66−22−220000000000000000000000000000
χ7444-4-444-4-4-20000-2222-22-200000000000000−2323−2323000000−2222000000006−66−62−22−20000000000000000000000000000
χ754-444-44-4-440000-44-44-4-44000000000000000000000022−22000000000022−22−222200000000000000000000000000000000
χ764-444-44-4-440000-44-44-4-440000000000000000000000−22220000000000−222222−2200000000000000000000000000000000
χ774-444-44-4-4-200002-22-222-20000000000000023−23−2323000022−220000000000−222−26−6−660000000000000000000000000000
χ784-444-44-4-4-200002-22-222-20000000000000023−23−23230000−222200000000002−2−22−666−60000000000000000000000000000
χ794-444-44-4-4-200002-22-222-200000000000000−232323−23000022−220000000000−222−2−666−60000000000000000000000000000
χ804-444-44-4-4-200002-22-222-200000000000000−232323−230000−222200000000002−2−226−6−660000000000000000000000000000
χ814-44-44-4-44-24-4-442-2-22-222004i−4i4i−4i0000002-20000-22000000−2i2i−2i2i0000000000000000000000000000000000000000
χ824-44-44-4-44-24-4-442-2-22-22200−4i4i−4i4i0000002-20000-220000002i−2i2i−2i0000000000000000000000000000000000000000
χ834-44-44-4-44-2-444-42-2-22-2220000004i−4i4i−4i00-2200002-20000000000−2i2i−2i2i000000000000000000000000000000000000
χ844-44-44-4-44-2-444-42-2-22-222000000−4i4i−4i4i00-2200002-200000000002i−2i2i−2i000000000000000000000000000000000000
χ854-4-444-44-440000-4-4-4444-40000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ864-4-444-44-440000-4-4-4444-400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ874-4-4-4-4444-244-4-422-222-2-24-4000000004-422-2-222-2-2-22000000000000000000000000000000000000000000000000
χ884-4-4-4-4444-244-4-422-222-2-2-4400000000-442222-2-2-2-22-2000000000000000000000000000000000000000000000000
χ89888-8-8-88-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).